A perturbation-theoretic procedure is developed for obtaining the spatial function Φ0 for the many-electron problem, from which the total wave function can be projected by the relation Ψ=iD~i0(r)Di0(σ)Φ0(r)χ0(σ). This function is expanded in a perturbation series in which the Φ00 contains a sufficient set of pair symmetries of Φ0 itself, such as in the Hartree nonantisymmetrized wave function for closed-shell atoms. When the expansion converges, the remaining symmetries are introduced exactly. The energy eigenvalue does not contain the usual "exchange" terms, since the zeroth-order Hamiltonian, unlike the Hartree-Fock H0, has no degeneracies. Applications to interaction energies in molecular crystals and asymmetric wave functions are discussed briefly.